We say that \(\sigma \)  contains a \(k\) -grid if its permutation matrix contains a \(k\) -grid.
When this is the case, any permutation in \(\mathfrak {S}_k\)  is a pattern of \(\sigma \) .
An example of permutation with a grid is the permutation \(\sigma \)  on \(k^2\)  elements
defined by \(\sigma (ki + j + 1) = kj + i + 1\)  for any \(0 \leqslant i,j < k\) .
Grids in permutations are deeply related to pattern-closed classes of permutations,
which are precursors of the work on twin-width,
see Marcus and Tardos [1]} and Guillemot and Marx [2]}.
